Self-guided beams in a diffractive χ(2) medium: variational approach

Victoria V. Steblina*, Yuri S. Kivshar, Mietek Lisak, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


It is demonstrated that the (1+1)- and (2+1)-dimensional self-guided beams (two-wave parametric spatial solitons) in a diffractive dielectric medium with purely quadratic nonlinearity (the so-called χ(2) material) can be effectively approximated by means of a familiar variational approach. In particular, for the physical conditions for which no analytical solutions exist, the variational approach yields Gaussian approximations of the (1+1) beams such that the ratio of the harmonic energy to the total beam energy equals, with ∼ 0.1% error, to the ratio obtained numerically.

Original languageEnglish
Pages (from-to)345-352
Number of pages8
JournalOptics Communications
Issue number3-4
StatePublished - 15 Jul 1995


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